A Verified Decision Procedure for Orders in Isabelle/HOL

Stevens, Lukas; Nipkow, Tobias

doi:10.1007/978-3-030-88885-5_9

Cited by 3 publications

(1 citation statement)

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“…This procedure, though, uses reflection to work on goals in Isabelle/HOL, which, during execution, either sacrifices speed by going through the simplifier or soundness by trusting generated code. More recently, Stevens and Nipkow [24] presented a verified decision procedure for orders that produces certificates. This approach offers efficient execution by using generated code as well as soundness as the certificates are replayed through Isabelle's inference kernel.…”

Section: Introductionmentioning

confidence: 99%

Towards a Verified Prover for a Ground Fragment of Set Theory

Stevens¹

2022

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Using Isabelle/HOL, we verify the state-of-the-art decision procedure for multi-level syllogistic with singleton (MLSS for short), which is a ground fragment of set theory. We formalise the syntax and semantics of MLSS as well as a sound and complete tableau calculus for it. We also provide an abstract specification of a decision procedure that applies the rules of the calculus exhaustively and prove its termination.

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